The Dynamic Bifurcation for the Granulation Convection in Cylindrical Coordinates

Abstract

This work formulates the simplified governing equations for granulation convection system in cylindrical coordinates by using the differential operator theory on Riemann manifold. We consider the case where the granulation convection system is under the influence of the control parameters R and E, Where R depends on the temperature difference and E is related to the magnetic field. Furthermore, we show that the simplified governing equations bifurcate from a trivial steady state solution, as the control parameters cross certain critical values. Notably, we are able to derive a RE-phase diagram in the case of two control parameters R and E, compared with the system without the influence of the control parameter E. In addition, our research shows that the difference of temperature and the magnetic field both accelerates the granulation convection.